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Block #2,646,158

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/3/2018, 5:44:11 AM Β· Difficulty 11.7455 Β· 4,190,596 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
e866403ad4490c613ffda743691437c2540dcf692c3d6a7cd439567d36366ee9
View on Chainz β†—

Height

#2,646,158

Difficulty

11.745522

Transactions

1

Size

199 B

Version

2

Bits

0bbeda86

Nonce

235,812,940

Timestamp

5/3/2018, 5:44:11 AM

Confirmations

4,190,596

Mined by

⛏️ P2SHAe8AbEzmgDSBZZWzcmyWVhxG4VJs4KqsZ9

Merkle Root

1c4b9aae7dc96df2d4ee0081536e234eda9528aedbcfae9407275dbaadf1eb9f
Transactions (1)
Coinbase1c4b9aae7dc96d…275dbaadf1eb9f
1 in β†’ 1 out7.2400 XPM109 B
Ae8AbEzm…Js4KqsZ9
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.269 Γ— 10⁹⁡(96-digit number)
12692070755668698221…20534084988513414401
Discovered Prime Numbers
p_k = 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
1.269 Γ— 10⁹⁡(96-digit number)
12692070755668698221…20534084988513414401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.538 Γ— 10⁹⁡(96-digit number)
25384141511337396442…41068169977026828801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.076 Γ— 10⁹⁡(96-digit number)
50768283022674792885…82136339954053657601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.015 Γ— 10⁹⁢(97-digit number)
10153656604534958577…64272679908107315201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.030 Γ— 10⁹⁢(97-digit number)
20307313209069917154…28545359816214630401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.061 Γ— 10⁹⁢(97-digit number)
40614626418139834308…57090719632429260801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.122 Γ— 10⁹⁢(97-digit number)
81229252836279668617…14181439264858521601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.624 Γ— 10⁹⁷(98-digit number)
16245850567255933723…28362878529717043201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.249 Γ— 10⁹⁷(98-digit number)
32491701134511867446…56725757059434086401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.498 Γ— 10⁹⁷(98-digit number)
64983402269023734893…13451514118868172801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.299 Γ— 10⁹⁸(99-digit number)
12996680453804746978…26903028237736345601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,938,318 XPMΒ·at block #6,836,753 Β· updates every 60s
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